Problem: Simplify the following expression: $ n = \dfrac{-4}{3} - \dfrac{6k + 8}{2k + 2} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2k + 2}{2k + 2}$ $ \dfrac{-4}{3} \times \dfrac{2k + 2}{2k + 2} = \dfrac{-8k - 8}{6k + 6} $ Multiply the second expression by $\dfrac{3}{3}$ $ \dfrac{6k + 8}{2k + 2} \times \dfrac{3}{3} = \dfrac{18k + 24}{6k + 6} $ Therefore $ n = \dfrac{-8k - 8}{6k + 6} - \dfrac{18k + 24}{6k + 6} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{-8k - 8 - (18k + 24) }{6k + 6} $ Distribute the negative sign: $n = \dfrac{-8k - 8 - 18k - 24}{6k + 6}$ $n = \dfrac{-26k - 32}{6k + 6}$ Simplify the expression by dividing the numerator and denominator by 2: $n = \dfrac{-13k - 16}{3k + 3}$